Math::BigFloat - Arbitrary size floating point math package use Math::BigFloat; # Number creation $x = Math::BigInt->new($str); # defaults to 0 $nan = Math::BigInt->bnan(); # create a NotANumber $zero = Math::BigInt->bzero();# create a "+0" # Testing $x->is_zero(); # return whether arg is zero or not $x->is_nan(); # return whether arg is NaN or not $x->is_one(); # true if arg is +1 $x->is_one('-'); # true if arg is -1 $x->is_odd(); # true if odd, false for even $x->is_even(); # true if even, false for odd $x->is_positive(); # true if >= 0 $x->is_negative(); # true if < 0 $x->is_inf(sign) # true if +inf or -inf (sign default '+') $x->bcmp($y); # compare numbers (undef,<0,=0,>0) $x->bacmp($y); # compare absolutely (undef,<0,=0,>0) $x->sign(); # return the sign, either +,- or NaN # The following all modify their first argument: # set $x->bzero(); # set $i to 0 $x->bnan(); # set $i to NaN $x->bneg(); # negation $x->babs(); # absolute value $x->bnorm(); # normalize (no-op) $x->bnot(); # two's complement (bit wise not) $x->binc(); # increment x by 1 $x->bdec(); # decrement x by 1 $x->badd($y); # addition (add $y to $x) $x->bsub($y); # subtraction (subtract $y from $x) $x->bmul($y); # multiplication (multiply $x by $y) $x->bdiv($y); # divide, set $i to quotient # return (quo,rem) or quo if scalar $x->bmod($y); # modulus $x->bpow($y); # power of arguments (a**b) $x->blsft($y); # left shift $x->brsft($y); # right shift # return (quo,rem) or quo if scalar $x->blog($base); # logarithm of $x, base defaults to e # (other bases than e not supported yet) $x->band($y); # bit-wise and $x->bior($y); # bit-wise inclusive or $x->bxor($y); # bit-wise exclusive or $x->bnot(); # bit-wise not (two's complement) $x->bround($N); # accuracy: preserver $N digits $x->bfround($N); # precision: round to the $Nth digit # The following do not modify their arguments: bgcd(@values); # greatest common divisor blcm(@values); # lowest common multiplicator $x->bstr(); # return string $x->bsstr(); # return string in scientific notation $x->exponent(); # return exponent as BigInt $x->mantissa(); # return mantissa as BigInt $x->parts(); # return (mantissa,exponent) as BigInt $x->length(); # number of digits (w/o sign and '.') ($l,$f) = $x->length(); # number of digits, and length of fraction All operators (inlcuding basic math operations) are overloaded if you declare your big floating point numbers as $i = new Math::BigFloat '12_3.456_789_123_456_789E-2'; Operations with overloaded operators preserve the arguments, which is exactly what you expect.

Canonical notation
Input to these routines are either BigFloat objects, or strings of the following four forms: `/^[+-]\d+$/' `/^[+-]\d+\.\d*$/' `/^[+-]\d+E[+-]?\d+$/' `/^[+-]\d*\.\d+E[+-]?\d+$/' all with optional leading and trailing zeros and/or spaces. Additonally, numbers are allowed to have an underscore between any two digits. Empty strings as well as other illegal numbers results in 'NaN'. bnorm() on a BigFloat object is now effectively a no-op, since the numbers are always stored in normalized form. On a string, it creates a BigFloat object.

Output
Output values are BigFloat objects (normalized), except for bstr() and bsstr(). The string output will always have leading and trailing zeros stripped and drop a plus sign. `bstr()' will give you always the form with a decimal point, while `bsstr()' (for scientific) gives you the scientific notation. Input bstr() bsstr() '-0' '0' '0E1' ' -123 123 123' '-123123123' '-123123123E0' '00.0123' '0.0123' '123E-4' '123.45E-2' '1.2345' '12345E-4' '10E+3' '10000' '1E4' Some routines (`is_odd()', `is_even()', `is_zero()', `is_one()', `is_nan()') return true or false, while others (`bcmp()', `bacmp()') return either undef, <0, 0 or >0 and are suited for sort. Actual math is done by using BigInts to represent the mantissa and exponent. The sign `/^[+-]$/' is stored separately. The string 'NaN' is used to represent the result when input arguments are not numbers, as well as the result of dividing by zero.

`mantissa()', `exponent()' and `parts()'
`mantissa()' and `exponent()' return the said parts of the BigFloat as BigInts such that: $m = $x->mantissa(); $e = $x->exponent(); $y = $m * ( 10 ** $e ); print "ok\n" if $x == $y; `($m,$e) = $x->parts();' is just a shortcut giving you both of them. A zero is represented and returned as `0E1', not `0E0' (after Knuth). Currently the mantissa is reduced as much as possible, favouring higher exponents over lower ones (e.g. returning 1e7 instead of 10e6 or 10000000e0). This might change in the future, so do not depend on it.

Accuracy vs. Precision
See also: Rounding. Math::BigFloat supports both precision and accuracy. For a full documentation, examples and tips on these topics please see the large section in the Math::BigInt manpage. Since things like sqrt(2) or 1/3 must presented with a limited precision lest a operation consumes all resources, each operation produces no more than `Math::BigFloat::precision()' digits. In case the result of one operation has more precision than specified, it is rounded. The rounding mode taken is either the default mode, or the one supplied to the operation after the scale: $x = Math::BigFloat->new(2); Math::BigFloat::precision(5); # 5 digits max $y = $x->copy()->bdiv(3); # will give 0.66666 $y = $x->copy()->bdiv(3,6); # will give 0.666666 $y = $x->copy()->bdiv(3,6,'odd'); # will give 0.666667 Math::BigFloat::round_mode('zero'); $y = $x->copy()->bdiv(3,6); # will give 0.666666

Rounding
Rounds to the $scale'th place left from the '.', counting from the dot. The first digit is numbered 1. Rounds to the $scale'th place right from the '.', counting from the dot. Rounds to an integer. Preserves accuracy to $scale digits from the left (aka significant digits) and pads the rest with zeros. If the number is between 1 and -1, the significant digits count from the first non-zero after the '.' These are effetively no-ops. All rounding functions take as a second parameter a rounding mode from one of the following: 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'. The default rounding mode is 'even'. By using `Math::BigFloat::round_mode($round_mode);' you can get and set the default mode for subsequent rounding. The usage of `$Math::BigFloat::$round_mode' is no longer supported. The second parameter to the round functions then overrides the default temporarily. The `as_number()' function returns a BigInt from a Math::BigFloat. It uses 'trunc' as rounding mode to make it equivalent to: $x = 2.5; $y = int($x) + 2; You can override this by passing the desired rounding mode as parameter to `as_number()': $x = Math::BigFloat->new(2.5); $y = $x->as_number('odd'); # $y = 3 # not ready yet After `use Math::BigFloat ':constant'' all the floating point constants in the given scope are converted to `Math::BigFloat'. This conversion happens at compile time. In particular perl -MMath::BigFloat=:constant -e 'print 2E-100,"\n"' prints the value of `2E-100'. Note that without conversion of constants the expression 2E-100 will be calculated as normal floating point number. The following does not work yet: $m = $x->mantissa(); $e = $x->exponent(); $y = $m * ( 10 ** $e ); print "ok\n" if $x == $y; There is no fmod() function yet. Both stringify and bstr() now drop the leading '+'. The old code would return '+1.23', the new returns '1.23'. See the documentation in the Math::BigInt manpage for reasoning and details. The following will probably not do what you expect: print $c->bdiv(123.456),"\n"; It prints both quotient and reminder since print works in list context. Also, bdiv() will modify $c, so be carefull. You probably want to use print $c / 123.456,"\n"; print scalar $c->bdiv(123.456),"\n"; # or if you want to modify $c instead. Beware of: $x = Math::BigFloat->new(5); $y = $x; It will not do what you think, e.g. making a copy of $x. Instead it just makes a second reference to the same object and stores it in $y. Thus anything that modifies $x will modify $y, and vice versa. $x->bmul(2); print "$x, $y\n"; # prints '10, 10' If you want a true copy of $x, use: $y = $x->copy(); See also the documentation in the overload manpage regarding `='. `bpow()' now modifies the first argument, unlike the old code which left it alone and only returned the result. This is to be consistent with `badd()' etc. The first will modify $x, the second one won't: print bpow($x,$i),"\n"; # modify $x print $x->bpow($i),"\n"; # ditto print $x ** $i,"\n"; # leave $x alone This program is free software; you may redistribute it and/or modify it under the same terms as Perl itself. Mark Biggar, overloaded interface by Ilya Zakharevich. Completely rewritten by Tels http://bloodgate.com in 2001.